ConwayLife.com

This is intended to be a list of circuit rules, computers, and other things pertaining to digital logic in cellular automata so that people can see the prior work. It is not a list of turing complete systems; this is more about practical computation. The systems are marked as HIGH, MID, or LOW depending on how abstract and easy to use they are. HIGH ones are easy, LOW ones are hard. I have provided the names of people if I have their real names; otherwise I'd just be copying their username from the thread and you could see that yourself. Thanks to ishanpm for 3 of the system descriptions, yoel for suggesting Fireworld(2) and FreeElectronics, Redstoneboi for suggesting Sticky, Flow6, and F6RIE, and islptng for suggesting NORworld.

I encourage others to suggest systems and computers I've missed, details I've left out in my descriptions, or mistakes I've made/suggestions etc.

The computation compilation: Compcomp.
Systems

MID Wireworld (1987) Brian Silverman
Incredibly simple 4-state CA based on electrons interacting in nontrivial ways. Implemented by many programs.

LOW Fireworld (2001) Yoel Matveyev
Photon-based rule, somewhat similar to Star Wars (345/2/4). Originally implemented in Mirek's Cellebration. Can be run in Golly, or any simulator that supports the notation of its rulestring, "03ajkr/2ak/3".

HIGH Circuitry Simulator (2009) Jack Eisenmann*
A simulator with instant wire and discrete signals, using the opening and closing of "gates" (not to be confused with "logic gates") to perform computations, implemented in Flash.

MID Wave (2010)
12-state CA where the basic unit of computation is a configurable AND/ANDNOT gate. Uses an interesting system where gates handle signals continuously, although this makes it somewhat difficult to work with. Implemented in Golly. (Description by ishanpm.)

MID WWEJ3 (2010)
An 18-state extension of WireWorld that allows for universal construction. Uses 8 types of electrons that allow a wire to act like a construction arm. Implemented in Golly. (Description by ishanpm.)

HIGH Logic Land (2012) Jack Eisenmann
(thread here) Somewhat complex but very intuitive 17-state CA based on continous signals going through wires, and simple logic gates. Currently impossible to create in Golly; the only two implementations are the one linked above and this.

MID Bliptile (2012)
(see 1, 2) Simple 4-state rule similar to Wireworld (though apparently created independently).

HIGH LLLL (2014-2015) Lode Vandevenne
Complicated 33-state CA based on continous signals and logic gates made out of different media through which a signal can pass. Allows a small crossover. Implemented in Golly. Very good documentation.

HIGH Rychládrát (2016) ME!*
A rule that I made which has simple instant wire and is relatively high-level. Can currently be simulated only by Reasoning Realm, and a Golly Lua script which is much faster.

MID VarLife (2016)
Almost but not entirely unlike Life.

HIGH Logic Land 2 (2016) Jack Eisenmann*
Not really a cellular automaton; contains instant wire. Interesting to note is that a signal will travel through multiple gates in one tick, as such performing arbitrary computation instantly, given enough gates to go through. Incredibly high-level. Only one implementation.

HIGH 'Digital Circuit Simulator Rule' (2017)
32-state CA based on continuous signals and logic gates, whose function is determined by a specific cell indicating the logical operation to be performed. Contains states that allow for a 1-cell crossover. (I'm not really sure what to call it; the name seems purely descriptive and the rule itself is "Digital". Also, the ripple carry adder in the download in that thread was made by me, but no credit is given. :(). Implemented in Golly.

LOW FreeElectronics (2017)
4-state photon-based rule with universal construction.

HIGH Pulse2 (2017-2018)
A rule based on electrons flowing through wires and interacting with gates, which themselves act like wires transmitting continuous signals, it's kind of interesting. Implemented in Golly.

MID Wire2 (2018) ME!!
A rule based on electrons passing through 2-cell wide wires discovered by me messing around in this rulespace using Reasoning Realm. Somewhat novel.

MID Flow6 (2018-2022)
6-state rule with compact circuitry similar to Bliptile, and with universal construction. Very compact crossovers.

MID Sticky (2018-2021)
4-state photon-based rule with universal construction, similar to FreeElectronics. Can emulate Bliptile. Implemented in Golly.

MID No Time At All (2018)
A rule in which signals, each of which can be one of two colours, move along wires until they reach junctions at specific angles, at which point they wait for other signals to arrive. The main purpose of the rule is to eliminate timing problems from circuit design. Implemented in Golly.

MID Wireworld Modern (2019) Jeremy Tan
A 9-state extension of WireWorld focused on tight construction of logic gates. Has positive and negative electrons that perform various logical operations when they interact, depending on the angle. Implemented in Golly. (Description by ishanpm.)

HIGH DECA (2019)
7-state rule with discrete electrons and 1-cell 'toggle' components that allow or disallow them to pass. They can also collide destructively. 3x3 asynchronous crossover. Implemented in Golly.

HIGH LogicWorld (2010-2020) Mark Jeronimus
A rule with continuous signals and 1-cell logic gates, which take inputs from diagonal neighbours and output to orthogonal ones. Crossovers quite versatile and allow for logic to be compacted. Posted in 2020. Implemented in Golly.

MID GLogic (2020)
A simple rule based on continuous streams of photons destructively colliding. Has the constraint that the falling end of a signal can cause a 'backfire', which must be accounted for in circuit design; a version without backfire also exists. Implemented in Golly.

MID Fireworld2 (2020) Yoel Matveyev
Superset of Fireworld that includes unchanging "wire" cells that can be added to create static circuits. Much of the circuitry constructed in this rule uses an interesting model: 1 pilot bit is sent to "activate" a component, which then starts a clock that operates on the next n bits (for some n which is wired into the circuit). This simplifies timing. Also see Wilfred.

HIGH Semaphore (2022)
A 7-state circuitry rule that allows for compact crossovers without a specialised crossover state; logic is based on 'semaphore' states, which can be used to make compact logic gates and latches.

HIGH NORworld2 (2024)
A Moore-neighbourhood rule which allows for compact circuitry and compact signals. Cross-overs and logic gates are small and simple. The linked thread also has some variants of the rule with fewer states and/or more compact circuitry.

*Infinite speed of light, thus arguably not a CA
Computers

The Wireworld Computer (Wireworld, 1990-1992) "...David Moore and Mark Owen, with the help of many others..."
Likely the first 'real' computer in a cellular automaton. 16-bit TTA with 64 words of memory (52 generic), which gives it 1/8kb of ram. There is a really deep analysis here, although the English isn't all that great so hopefully you speak French. A browser simulation which allows the user to enter data into the machine is described here, available here (the blog post implies you have to use hexadecimal, but it just uses parseInt() so decimal can be used). I have created a programming language and several programs for this computer, available here.

Dick (Logic Land, 2016) ME!!!
Inspired very heavily by the Wireworld Computer. Much like the Wireworld computer, it is a 16-bit TTA with 5 7-segment displays showing an unsigned 16-bit number. It has 510.75 bytes (~0.5kb) of RAM.

Duverivý (Rychládrát, 2016) ME!!!!
(see 1) An 8-bit computer inspired mostly by Jack Eisenmann's DUO Adept, so it's his fault that the machine code is kinda inefficient. I didn't really understand the idea of registers, so (much like the DUO Adept (and Dick (and the Wireworld Computer))) all variables must be stored in RAM. It has 256 bytes (0.25kb) of RAM, 8 bytes of VRAM, an 8 bit PC, and 1 bit storing a "flag", used for conditionals. It has 6 buttons you can use for input, has an assembler and emulator, and several programs written for it. The name simply means computer in Czech.

'Programmable Computer' (B3/S23, 2016)
An 8-bit computer created in the game of life. It has 32 21-bit items of ROM to store a program, and 8 8-bit registers to use as variables (one of these registers is the PC). Has a simple display, showing a byte in binary, and a script to allow it to be programmed. An upgraded version was posted on 2021-10-12, with a more advanced instruction set and display (including a 2d graphics demo, drawing a circle).

The QFT Computer (Varlife, 2017)
Relatively fast and powerful computer; fast enough that you can simulate it and play Tetris by writing data into memory in real time, and see the game visually in RAM. Very well documented.

'Multicore Processor' (Pulse2, 2018)
16-bit simple processor, inspired very heavily by Zachtronics, which is evident in the way that it seems to be used as multiple very simple processors joined together to form a more complex algorithm. Each CPU contains 64 words of ROM (1/8kb), to store its program, and four 16-bit registers. I'm not really sure what to call it; it doesn't really seem to have much of a name.

DECA-Picoblaze (DECA, 2019)
8-bit processor with 16 8-bit registers, 1024 18-bit words of instruction ROM. It has 6 7-segment displays for output, but no binary-to-BCD conversion circuitry, so conversion must be done in software; alternatively they can display hexadecimal digits. Also has a 3-hex-digit display which shows the value of the program counter. I believe this is the first computer on this list which is based on a pre-existing instruction set, rather than implementing its own. Squiggly.

Izhora 1 (Fireworld2, 2021) Yoel Matveyev
32-bit SUBLEQ OISC processor with 64k 32-bit instruction words = 256kb of RAM. 128*64 and 256*128 memory-mapped pixel displays exist, which can be written to 32 bits at a time. Also has a keyboard peripheral.

S1K (Semaphore, 2022)
Tiny CPU; bounding box 91*94 cells. 16-bit Harvard architecture SUBLEQ OISC; 64 16-bit words of memory, half of which is RAM; the other half is ROM. Size given is of CPU itself with no display; including the display it's much bigger.

LEAST (Semaphore, 2023)
Even smaller CPU along the lines of S1K; 98*62 cells (this means S1K is still the smallest measured by bounding square). Same amount of memory (128 bytes). 8-bit. Has interactive program with buttons you can press. Size given is of entire CPU, including display and input buttons.

droid-logica (Star Wars (345/2/4), 2024)
32-bit CPU with unusual instruction set. RAM size is indeterminate, presumably as much as you care to add. Memory is addressed in 32-bit words. Not an OISC - in fact, it has separate AND and XOR - but it is nonetheless a limiting instruction set. There is no way to dereference a pointer, even an immediate one, so any non-trivial code must be self-modifying. Flow control is basically done using writes to a JMP target. Good documentation.

323 (B3/S23, 2023-2024) ME!!!!!
A 32-bit computer designed to run quickly when simulated with the HashLife algorithm. RISC-like architecture with 16 registers, 14 of which are GPRs. The architecture was designed to be easy to program, and it has multiplication and division instructions. It also has an instruction cache, 32x32 display, and keyboard peripheral to take inputs from the user. It can do text rendering and Tetris, although they are both slow. Has thorough documentation with plenty of example programs and an intro video inspired by Jack Eisenmann.

Honourable mentions
All of the turing complete machines in the game of life:
A Turing Machine (2000) Paul Rendell
The Minsky Register Machine (2002) Paul Chapman
Spartan Universal Computer-Constructor (2009) Adam P. Goucher
'Turing Machine Simulator' (2018); another turing machine made years later is mentioned in that thread.
And one in Flow6:
The Flow6 Read-If/Else System (F6RIE) (2022)

This thing.

The Powder Toy has had plenty of computers created in it. I personally like this.

I would very much appreciate any assistance in expanding or improving this list, including writing your own sections on things or correcting mistakes or whatever.

(edit 1: added the powder toy) (edit 2 (2018-04-21): the url tag for the MRM no longer takes up the whole line) (edit 3 (2018-04-29): Added Wire2.) (edit 4 (2018-06-30): Changed link for Pulse2 to lead to a thread.) (edit 5 (2018-10-06): Corrected statement about Dick's memory size (two words have one bit missing), wrote description of "Circuitry Simulator", miscellaneous copy-edits.) (edit 6 (2018-12-19): added link to Wireworld Computer simulator and changed description of its RAM.) (edit 7 (2019-01-17): added descriptions for Wave, WWEJ3, and WireWorld Modern contributed by ishanpm, added mention of BWCSL, fixed parenthesis on the Pulse2 computer.) (edit 8 (2019-01-20): WWC has 52 generic words, not 51.) (edit 9 (2019-01-21): added links to Rychládrát and Duverivý documentation.) (edit 10 (2019-01-25): added Freywa's name.) (edit 11 (2019-05-27): added NTAA.) (edit 12 (2020-06-14): added GLogic.) (edit 13 (2020-06-28): added LogicWorld, mentioned no-backfire version of GLogic.) (edit 14 (2020-10-28): added DECA and its computer.) (edit 15 (2020-10-29): added Fireworld and FreeElectronics.) (edit 16 (2020-10-30): Fireworld was 2001, not 2002.) (edit 17 (2020-12-02): mentioned and linked Lua script for Rychládrát.) (edit 18 (2021-07-01): added Sticky, added HIGH/MID/LOW to system descriptions to indicate level of abstraction) (edit 19 (2021-10-08): added Fireworld2 and Izhora 1.) (edit 20 (2021-10-13): added (2) after "Fireworld".) (edit 21 (2021-10-18): added link to Coban's upgraded B3/S23 computer.) (edit 22 (2022-01-25): mentioned features of Izhora 1b.) (edit 23 (2022-12-13): added VarLife, added QFT computer, added Semaphore, added S1K.) (edit 24 (2022-12-15): added Flow6, added F6RIE to honourable mentions.) (edit 25 (2022-12-16): made years for Flow6 and Sticky more accurate.) (edit 26 (2022-12-18): fixed dead link to WWC analysis.) (edit 27 (2023-07-22): removed redundant mention of QFT computer.) (edit 28 (2023-09-16): added LEAST.) (edit 29 (2024-04-21): added droid-logica, removed honourable mention for Star Wars since it's now redundant.) (edit 30 (2024-11-22): mentioned Turing machine by AlbertArmStain.) (edit 31 (2025-01-16): added 323 and NORworld2.) (edit 32 (2025-01-16): fixed incorrect statement about NORworld2.) (edit 33 (2025-02-23): Semaphore has 7 states, not 6.)

P.S. It would be nice if people actually bothered to give their creations proper names more often.

I hope this isn't off topic, but would non-totalistic two state rules with computers in them be included? I ask because I may build a computer in Snowflakes, and I think you would like it, but the only non-ruletable rule here is Star Wars so I am wary on whether it would qualify

danny wrote:I hope this isn't off topic, but would non-totalistic two state rules with computers in them be included? I ask because I may build a computer in Snowflakes, and I think you would like it, but the only non-ruletable rule here is Star Wars so I am wary on whether it would qualify

I included Coban's 8-bit computer in the game of life, so yeah, if you make a computer in a Hensel rule (which is totally what they should call those) it will probably be included in the main list of computers.

Transers might be possible to build circuits in as well. Does anyone know of any logic gates in it as of now?

The QFT computer can be compiled to GOL (hypothetically).

fluffykitty wrote:The QFT computer can be compiled to GOL (hypothetically).

Yes, but if I make a B3/S23 Wireworld metacell does that mean that the Wireworld Computer is a computer in the game of life? I think that there's an unavoidable level of subjectivity in the finer details and distinctions here, and in my subjective opinion I think that the QFT computer was not created in B3/S23, but in its own wire automaton. I don't think that calling it a computer in the game of life really serves the purpose of the list; it does not describe the work that was done in practice.

Also, it's ugly.

Yay, my CA is kind of interesting! My mission is accomplished

The QFT computer might not really be in CGOL, but there's just something that tickles me about writing a game of Tetris inside a language that compiles to a machine language that's run on a computer designed in a CA that's modeled in metacells inside another CA.

Also, here are some more systems to add to your list:

Wave (2010)
12-state CA where the basic unit of computation is a configurable AND/ANT gate. Uses an interesting system where gates handle signals continuously, although this makes it somewhat difficult to work with. Implemented in Golly.

WWEJ3 (2010)
An 18-state extension of WireWorld that allows for universal construction. Uses 8 types of electrons that allow a wire to act like a construction arm. Implemented in Golly.

Wireworld Modern (2019)
A 9-state extension of WireWorld focused on tight construction of logic gates. Has positive and negative electrons that perform various logical operations when they interact, depending on the angle. Implemented in Golly.

Someone finally added to the list!
I remember intending to list VarLife as its own CA and then listing the QFT computer as a computer in that CA, but I never got around to it. Maybe at some point I will.

ishanpm wrote:Also, here are some more systems to add to your list:

Thanks. I'm going to add these, but the Wave description seems to have a typo or some obscure terminology I don't understand. What is an ANT gate? Did you mean ANDNOT gate?

blah wrote:What is an ANT gate? Did you mean ANDNOT gate?

Yeah, I mean ANDNOT. I've seen it referred to as ANT in a few places, but I can't find any examples.

The way Wave handles logic is pretty interesting. Every gate is a 4 by 4 block of cells, with some flags on the corners that indicate whether each side is a positive input, negative input, or output. The same shape is also used for crossovers. So an XOR might look like this:

WSwitch
WireWorldVonNeumann
PowderGdi
Cell builder

Self plug time
Tags: 4-state, Photons, Moore, Turing-Complete, Construction-Destruction-Universal, Practical?

More self-plug
Hutton32 minsky register machine

Update:

There is now a Golly script for the keyboard.

My Izhora computer has now a version with a 256x128 display and a keyboard, called Izhora 1b, and a version of the original one with the 128x64 display and a keyboard, called Izhora 1a.

https://github.com/yoelmatveyev/Izhora/ ... n/machines

There are Izhora 1b versions of "Hello world", Fibonacci numbers, primes and 128-bit factorials in my repo.

The keyboard is conditionally mapped by its controller to the memory address 0xFFFF. It's scanned once in every 6144 generations, matching the memory cycle rate (probably too fast; the scanning rate can be trivially slowed down). Once a non-zero scancode is received, it's stored in the controller's 8-bit register; further updates get blocked until the scancode gets written into the RAM.

If 0xFFFF contains 0, the keyboard controller writes the scancode to this address and gets ready for the next key scan. As long as 0xFFFF is not cleared to 0, the keyboard controller's register preserves the same scancode as the first key pressed.

The keyboard has 2 modifier keys: SHIFT and META. SHIFT is encoded as the 7th bit of the scancode and META as the 8th. Naturally, the scanning process clears the keyboard. Pressing a key is emulated by placing a dot in a particular uniform place in the middle of the key:
The scancode table is as follows:

ROW1: 12 59 42 25 8 55 38 21 4 51 34 17 META (+128)

ROW2: 41 24 7 54 37 20 3 50 33 16 63 46 29

ROW3: 6 53 36 19 2 49 32 15 62 45 28 11 58

ROW4: 35 18 1 48 31 14 61 44 27 10 57 40 23

ROW5: SHIFT (+64) 47 30 13 60 43 26 9 56 39 22 5 52

The video memory takes now 4k from 0x0400 to 0x07FF (addressed by 32-bit words). The display is little-endian and bottom-up, meaning that lower addresses are displayed lower, like in some bitmap image formats.

I am working now on a much more advanced RISC architecture, but as it is now, the computer is already totally practical, although things like bitwise logic and long multiplication require a few hundreds of operations. This particular variety of SUBLEQ seems quite suitable for implementing Forth or something similar. If the accumulator is kept negative or 0, subroutines can be densely referenced by single SUBLEQ commands, like threaded code in Forth engines.

Although Fireworld2 is not the easiest rule for building a computer, it seems to be the most simple one on this list along with Wireworld. To my knowledge, my computer is by far the only one implemented as CA that has capabilities of real-life computers from the 1980s. Something similar or bigger, of course, can be constructed using any rule mentioned in this thread. I would love to see other examples of "CA computing at large".

Strange that I didn't add this here but
Rule: Flow6
6-state Construction, 2019-2022, probably Mid-level since circuitry is primarily timing-based, but timing-agnostic circuits do exist, as demonstrated in the Computer dubbed the "Flow6 Read-If/Else System" whose acronym I'd like you to guess and use

Redstoneboi wrote: December 15th, 2022, 8:50 am (Flow6 and its Turing machine)

Thanks for your suggestions. I've added them both, although I only added the Read-If/Else machine to honourable mentions rather than the main computer list since, to me, it belongs more in the realm of theoretical computer science than normal CPU design. My general rule is that if a machine is Turing-complete, then it's not a computer, since computers only have finite memory spaces.

You might argue the same for the SUBLEQ machines Izhora-1 and S1K, since their instruction set is sort of esolangy, but they both have a more conventional fetch-execute cycle, which is the defining trait of computers.

Correction: Flow6 was made in June 22, 2018, even before Sticky in September 5 the same year, but most of the development happened in the Discord server, so pretty much nobody in the forums knew about it until I somehow ended up posting Sticky in 2018 and Flow6 in 2019.

Before Flow6, there was the Arms series of rules that were pretty much prototypes. I wouldn't recommend listing them as anything more than a footnote, but you can see that rule was posted in May 14. There was development even before then, when there were still 9 states, and probably back then there were 13 states and the wires were still blue when I first took inspiration from Devore.

Redstoneboi wrote: December 16th, 2022, 6:37 am Before Flow6, there was the Arms series of rules that were pretty much prototypes. I wouldn't recommend listing them as anything more than a footnote, but you can see that rule was posted in May 14.

The Arms rules do have one feature that others don't: two signals can pass through each other so you can have "extend+read" signals going one way down a read arm and the data coming back down the same wire, which would be impossible in most any other wiring rule.